>>if a model is factually wrong a claim with a source is checkable and a claim from weights isn't.

>Why? If a model's weights claim that Bart Simpson became President in 2020, why does this fact suddenly become uncheckable?

Because in one case you have a source you can use to validate the fact, and in the other you don't. Though, as you explain earlier in your comment, the premise is misguided/hallucinated.